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Discrete breathers in square lattices from delocalized nonlinear vibrational modes
E K Naumov1,2, Yu V Bebikhov3, E G Ekomasov4
1Institute of Molecule and Crystal Physics, UFRC of Russian Academy of Sciences, Ufa 450075, Russia.
Physical Review. E
|April 19, 2023
Summary
Researchers created long-lived quasibreathers in a lattice by modifying nonlinear vibrational modes. This method can be extended to find quasibreathers in 3D crystal lattices.
Area of Science:
- Condensed matter physics
- Nonlinear dynamics
- Lattice dynamics
Background:
- Discrete breathers (DBs) and intrinsic localized modes (ILMs) represent fundamental nonlinear phenomena in discrete systems.
- Delocalized nonlinear vibrational modes (DNVMs) have been previously identified in the β-Fermi-Pasta-Ulam-Tsingou (β-FPUT) lattice.
Purpose of the Study:
- To investigate the generation and characteristics of standing and moving discrete breathers in a 2D square β-FPUT lattice.
- To explore the potential of using DNVMs for creating localized vibrational modes.
Main Methods:
- Applying localizing functions to pre-existing delocalized nonlinear vibrational modes (DNVMs).
- Utilizing specific initial conditions to observe the evolution of these modes over time.
- Numerical simulations to analyze the stability and longevity of the generated quasibreathers.
Main Results:
- Successfully generated long-lived quasibreathers (approximations of discrete breathers) in the 2D square β-FPUT lattice.
- Demonstrated that quasibreathers can be obtained from DNVMs even when initial conditions are not exact solutions.
- Observed both standing and moving localized modes.
Conclusions:
- The method of applying localizing functions to DNVMs is effective for creating quasibreathers.
- This approach offers a viable pathway for searching for quasibreathers in more complex systems, including 3D lattices.
- The findings contribute to the understanding of nonlinear localized modes in discrete systems.
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